### Notes on Logic

I'm studying for a big exam, and I've been wondering what the *precise* definitions are of certain terms used in logical arguments. Thanks to Merriam-Webster OnLine, I now know. And you can too! (So don't ever say you never learn anything *useful* at Songdog.net).

A **lemma** is "an auxiliary proposition used in the demonstration of another proposition"

A **corollary** is "a proposition inferred immediately from a proved proposition with little or no additional proof"

An **axiom** is "**1** : a maxim widely accepted on its intrinsic merit; **2** : a statement accepted as true as the basis for argument or inference; **3** : an established rule or principle or a self-evident truth" (see also **postulate**)

A **theorem** is "**1** : a formula, proposition, or statement in mathematics or logic deduced or to be deduced from other formulas or propositions; **2** : an idea accepted or proposed as a demonstrable truth often as a part of a general theory" (see also **proposition**)

Incidentally, a **hypothesis** is "**1 a** : an assumption or concession made for the sake of argument **b** : an interpretation of a practical situation or condition taken as the ground for action; **2** : a tentative assumption made in order to draw out and test its logical or empirical consequences; **3** : the antecedent clause of a conditional statement"

The difference between a theorem and a hypothesis seems subtle: a theorem is something you will attempt to prove or at least deduce, while a hypothesis is something which you may attempt to test. And therein lies the difference between the methods of mathematics and of science.

By the way, did you know that a theorem is also "**3** : [a] stencil; **4** : a painting produced especially on velvet by the use of stencils for each color"?

## Comments

Furthermore, a theorem with a painting of Motorhead on it is a "lemma"; one that depicts the Thompson Twins is a "dilemma."

Posted by: steve | May 8, 2002 06:43 PM

Ah, Motörhead. I get the "Lemmy" reference, but I'm afraid I'm missing something with the Thompson Twins. Can you explain?

Personally, I was thinking of an Elvis theorem...

Posted by: Songdog | May 8, 2002 07:04 PM

Two of them. "Di"-lemma. Not very subtle or profound, I fear.

Posted by: steve | May 9, 2002 01:12 PM